Method of Moments Estimation for Rectangular Distribution

[grimster]

ok, X_1,X_2,...,X_n are independant(and unbiased) rectangular distributed random variables over the interval [0,a]

It is known that T(X)=max(X_1,X_2,...,X_n) is sufficient. i am supposed to find the moment estimator for a using the method of moments.

i know I'm supposed to equate the first k sample moments to the corresponding k population moments and solve the resulting system of equations, but i have a few questions:

1.is the rectangular distribution the same as the uniform distribution?

2.to get me started so i understand what to do, what is the first sample and population moment?

 

[grimster]

something like this:
sample moment = the population moment:
x_bar=a/2 -> a=2*x_bar